23.1.309 problem 298 (b)

Internal problem ID [4916]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 298 (b)
Date solved : Tuesday, September 30, 2025 at 08:56:32 AM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }&=-1-y^{2} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 11

ode:=(x^2+1)*diff(y(x),x) = -1-y(x)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\tan \left (\arctan \left (x \right )+c_1 \right ) \]

✓ Mathematica. Time used: 0.153 (sec). Leaf size: 29

ode=(1+x^2)*D[y[x],x]==-(1+y[x]^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\tan (\arctan (x)-c_1)\\ y(x)&\to -i\\ y(x)&\to i \end{align*}

✓ Sympy. Time used: 0.167 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x**2 + 1)*Derivative(y(x), x) + y(x)**2 + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \tan {\left (C_{1} - \operatorname {atan}{\left (x \right )} \right )} \]